What is the integral of 3x(5x^2+4)^9 ?

The integral of 3x(5x^2+4)^9 is 3/100 (5x^2+4)^{10}+C

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integral of 3x(5x^2+4)^9

\int 3 x (5 x^{2} + 4)^{9} d x

\frac{3}{100} (5 x^{2} + 4)^{10} + C

Solution steps

\int 3 x (5 x^{2} + 4)^{9} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int x (5 x^{2} + 4)^{9} d x

Apply u-substitution

: \int \frac{u ^{9}}{10} d u

= 3 \cdot \int \frac{u ^{9}}{10} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \frac{1}{10} \cdot \int u^{9} d u

Apply the Power Rule

: \frac{u ^{10}}{10}

= 3 \cdot \frac{1}{10} \cdot \frac{u ^{10}}{10}

Substitute back

u = 5 x^{2} + 4

= 3 \cdot \frac{1}{10} \cdot \frac{( 5 x ^{2} + 4 ) ^{10}}{10}

Simplify

3 \cdot \frac{1}{10} \cdot \frac{( 5 x ^{2} + 4 ) ^{10}}{10} : \frac{3}{100} (5 x^{2} + 4)^{10}

= \frac{3}{100} (5 x^{2} + 4)^{10}

Add a constant to the solution

= \frac{3}{100} (5 x^{2} + 4)^{10} + C

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What is the integral of 3x(5x^2+4)^9 ?
The integral of 3x(5x^2+4)^9 is 3/100 (5x^2+4)^{10}+C